arXiv subjects

Andrew Gould

Publications and source records attributed to Andrew Gould.

At least 289 records · Page 16Linked to original sources

arXiv2006

Black Hole Masses and Eddington Ratios at 0.3<z<4

We study the distribution of Eddington luminosity ratios, L_bol/L_edd, of active galactic nuclei (AGNs) discovered in the AGN and Galaxy Evolution Survey (AGES). We combine H-beta, MgII, and CIV line widths with continuum luminosities to estimate black hole (BH) masses in 407 AGNs, covering the redshift range z~0.3-4 and the bolometric luminosity range L_bol~10^45-10^47 erg/s. The sample consists of X-ray or mid-infrared (24 micron) point sources with optical magnitude R<=21.5 mag and optical emission line spectra characteristic of AGNs. For the range of luminosity and redshift probed by AGES, the distribution of estimated Eddington ratios is well described as log-normal with a peak at L_bol/L_edd ~ 1/4 and a dispersion of 0.3 dex. Since additional sources of scatter are minimal, this dispersion must account for contributions from the scatter between estimated and true BH mass and the scatter between estimated and true bolometric luminosity. Therefore, we conclude that: (1) neither of these sources of error can contribute more than \~0.3 dex rms; and (2) the true Eddington ratios of optically luminous AGNs are even more sharply peaked. Because the mass estimation errors must be smaller than ~0.3 dex, we can also investigate the distribution of Eddington ratios at fixed BH mass. We show for the first time that the distribution of Eddington ratios at fixed BH mass is peaked, and that the dearth of AGNs at a factor ~10 below Eddington is real and not an artifact of sample selection. These results provide strong evidence that supermassive BHs gain most of their mass while radiating close to the Eddington limit, and they suggest that the fueling rates in luminous AGNs are ultimately determined by BH self-regulation of the accretion flow rather than galactic scale dynamical disturbances.

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arXiv2006

Probing the Shape of the Galactic Halo with Hyper-Velocity Stars

Precise proper motion measurements (sigma_mu ~ 10 mkas/yr) of the recently discovered hyper-velocity star (HVS) SDSS J090745.0+024507 would yield significant constraints on the axis ratios and orientation of a triaxial model for the Galactic halo. Triaxiality of dark matter halos is predicted by Cold Dark Matter models of galaxy formation and may be used to probe the nature of dark matter. However, unless the distance to this star is determined to better than 10%, these constraints suffer from one-dimensional degeneracies, which we quantify. We show how proper motion measurements of several HVSs could simultaneously resolve the distance degeneracies of all such stars and produce a detailed picture of the triaxial halo. Additional HVSs may be found from radial velocity surveys or from parallax/proper-motion data derived from GAIA. High-precision proper-motion measurements of these stars using the Space Interferometry Mission (SIM PlanetQuest) would substantially tighten the constraints they yield on the Galactic potential.

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arXiv2006

Frequency of Hot Jupiters and Very Hot Jupiters from the OGLE-III Transit Surveys Toward the Galactic Bulge and Carina

We derive the frequencies of hot Jupiters (HJs) with 3--5 day periods and very hot Jupiters (VHJs) with 1-3 day periods by comparing the planets actually detected in the OGLE-III survey with those predicted by our models. The models are constructed following Gould & Morgan (2003) by populating the line of sight with stars drawn from the Hipparcos catalog. Using these, we demonstrate that the number of stars with sensitivity to HJs and VHJs is only 4--16% of those in the OGLE-III fields satisfying the spectroscopic-followup limit of V_max<17.5. Hence, the frequencies we derive are much higher than a naive estimate would indicate. We find that at 90% confidence the fraction of stars with planets in the two period ranges is (1/310)(1^{+1.39}_{-0.59}) for HJs and (1/690)(1^{+1.10}_{-0.54}) for VHJs. The HJ rate is statistically indistinguishable from that found in radial velocity (RV) studies. However, we note that magnitude-limited RV samples are heavily biased toward metal-rich (hence, planet-bearing) stars, while transit surveys are not, and therefore we expect that more sensitive transit surveys should find a deficit of HJs as compared to RV surveys. The detection of 3 transiting VHJs, all with periods less than 2 days, is marginally consistent with the complete absence of such detections in RV surveys. The planets detected are consistent with being uniformly distributed between 1.00 and 1.25 Jovian radii, but there are too few in the sample to map this distribution in detail.

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arXiv2005

Survey for Transiting Extrasolar Planets in Stellar Systems. II. Spectrophotometry and Metallicities of Open Clusters

We present metallicity estimates for seven open clusters based on spectrophotometric indices from moderate-resolution spectroscopy. Observations of field giants of known metallicity provide a correlation between the spectroscopic indices and the metallicity of open cluster giants. We use χ^2 analysis to fit the relation of spectrophotometric indices to metallicity in field giants. The resulting function allows an estimate of the target-cluster giants' metallicities with an error in the method of \pm0.08 dex. We derive the following metallicities for the seven open clusters: NGC 1245, [m/H]=-0.14\pm0.04; NGC 2099, [m/H]=+0.05\pm0.05; NGC 2324, [m/H]=-0.06\pm0.04; NGC 2539, [m/H]=-0.04\pm0.03; NGC 2682 (M67), [m/H]=-0.05\pm0.02; NGC 6705, [m/H]=+0.14\pm0.08; NGC 6819, [m/H]=-0.07\pm0.12. These metallicity estimates will be useful in planning future extra-solar planet transit searches since planets may form more readily in metal-rich environments.

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arXiv2005

Systematic Analysis of 22 Microlensing Parallax Candidates

We attempt to identify all microlensing parallax events for which the parallax fit improves Δχ^2 > 100 relative to a standard microlensing model. We outline a procedure to identify three types of discrete degeneracies (including a new one that we dub the ``ecliptic degeneracy'') and find many new degenerate solutions in 16 previously published and 6 unpublished events. Only four events have one unique solution and the other 18 events have a total of 44 solutions. Our sample includes three previously identified black-hole (BH) candidates. We consider the newly discovered degenerate solutions and determine the relative likelihood that each of these is a BH. We find the lens of event MACHO-99-BLG-22 is a strong BH candidate (78%), event MACHO-96-BLG-5 is a marginal BH candidate (37%), and MACHO-98-BLG-6 is a weak BH candidate (2.2%). The lens of event OGLE-2003-BLG-84 may be a Jupiter-mass free-floating planet candidate based on a weak 3 sigma detection of finite-source effects. We find that event MACHO-179-A is a brown dwarf candidate within ~100 pc of the Sun, mostly due to its very small projected Einstein radius, \tilde r_E = 0.23+-0.05 AU. As expected, these microlensing parallax events are biased toward lenses that are heavier and closer than average. These events were examined for xallarap (or binary-source motion), which can mimic parallax. We find that 23% of these events are strongly affected by xallarap.

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arXiv2005

E = mc^2 Without Relativity

The equivalence of mass and energy is indelibly linked with relativity, both by scientists and in the popular mind. I prove that E = mc^2 by demanding momentum conservation of an object that emits two equal electromagnetic wave packets in opposite directions in its own frame. In contrast to Einstein's derivation of this equation, which applies energy conservation to a similar thought experiment, the new derivation employs no effects that are greater than first order in v/c and therefore does not rely on results from Special Relativity. In addition to momentum conservation, it uses only aberration of starlight and the electromagnetic-wave momentum-energy relation p=E/c, both of which were established by 1884. In particular, no assumption is made about the constancy of the speed of light, and the derivation proceeds equally well if one assumes that light is governed by a Galilean transformation. In view of this, it is somewhat puzzling that the equivalence of mass and energy was not derived well before the advent of Special Relativity. The new derivation is simpler and more transparent than Einstein's and is therefore pedagogically useful.

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arXiv2005

Probing MACHOs Toward the Galactic Bulge

If the massive compact halo object (MACHO) fraction of the Galactic dark halo is f ~ 20% as suggested by some microlensing experiments, then about 1.2% of lensing events toward the Galactic bulge are due to MACHOs. For the 40% of these that lie nearby (D_l < 4 kpc), measurement of their distance D_l would distinguish them from bulge lenses, while measurement of their transverse velocity v_l would distinguish them from disk lenses. Hence, it would be possible to identify about 0.5%(f/20%) of all events as due to MACHOs. I show that a planned experiment using the Space Interferometry Mission (SIM PlanetQuest) could thereby detect 1 or 2 such events. This is at the margin of what is required because of a small, but non-negligible background from spheroid stars.

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arXiv2004

Halo Luminosity Function From Photometric Calibration of the Revised NLTT

We calibrate the photographic photometry of the revised New Luyten Two-Tenths catalog (rNLTT) by matching 3448 rNLTT stars to the Sloan Digital Sky Survey (SDSS). The correction is linear in magnitude and goes from zero at V ~ 14 to 0.32 mag at V=19, in the sense that rNLTT was previously too bright. The correction implies that the underlying USNO-A2.0 photometry, on which rNLTT photometry is based, is non-linear. The new calibration somewhat improves the appearance of the (V,V-J) reduced proper motion diagram in the sense of better separation between disk and halo stars. We repeat Gould's analysis of 5000 halo stars in rNLTT. The most important change is to move the peak of the halo luminosity function about 0.5 mag dimmer, from M_V=10.5 to M_V=11, putting it into good agreement with the parallax-based determination of Dahn et al.

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arXiv2004

Microlensing Characterization of Wide-Separation Planets

With their excellent photometric precision and dramatic increase in monitoring frequency, future microlensing survey experiments are expected to be sensitive to very short time-scale, isolated events caused by free-floating and wide-separation planets with mass as low as a few lunar masses. We estimate the probability of measuring the Einstein radius θ_E for bound and free-floating planets. We carry out detailed simulations of the planetary events expected in next-generation surveys and estimate the resulting uncertainty in θ_E for these events. We show that, for main-sequence sources and Jupiter-mass planets, the caustic structure of wide-separation planets with projected separations of < 20 AU substantially increases the probability of measuring the dimensionless source size and thus determining θ_E compared to the case of unbound planets. In this limit where the source is much smaller than the caustic, the effective cross-section to measure θ_E to 10% is ~25% larger than the full width of the caustic. Measurement of the lens parallax is possible for low-mass planetary events by combined observations from the ground and a satellite located in an L2 orbit; this would complete the mass measurements for such wide-separation planets. Finally, short-duration events caused by bound planets can be routinely distinguished from those caused by free-floating planets for planet-star separations < 20 AU from either the deviations due to the planetary caustic or (more often) the low-amplitude bump from the magnification due to the parent star.

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arXiv2004

Prospects for the Detection of Earth-Mass Planets

We compare potential state-of-the-art experiments for detecting Earth-mass planets around main-sequence stars using radial velocities, transits, astrometry, and microlensing. For conventionally-discussed signal-to-noise ratio (S/N) thresholds, S/N ~ 8, the last three methods are roughly comparable in terms of both the total number of planets detected and the mass distribution of their host stars. However we argue that S/N ~ 25 is a more conservative and realistic S/N threshold. We show analytically and numerically that the decline in the number of detections as a function of S/N is very steep for radial velocities, transits, and astrometry, such that the number of expected detections at S/N ~ 25 is more than an order-of-magnitude smaller than at conventional S/N thresholds. Indeed, unless Earth-mass planets are very common or are packed much closer to their parent stars than in the solar system, future searches using these methods (as they are currently planned) may not yield any reliable Earth-mass planet detections. On the other hand, microlensing has a much shallower S/N slope than the other techniques and so has much greater sensitivity at realistic S/N thresholds. We show that even if all stars have Earth-mass planets at periods of one year (and adopting other optimistic assumptions as well), the combined yield of all four techniques would be the detection of only about five such planets at S/N ~ 25.

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arXiv2004

The Mass of the MACHO-LMC-5 Lens Star

We combine the available astrometric and photometric data for the 1993 microlensing event MACHO-LMC-5 to measure the mass of the lens, M=0.097 +/- 0.016 Msun. This is the most precise direct mass measurement of a single star other than the Sun. In principle, the measurement error could be reduced as low as 10% by improving the trig parallax measurement using, for example, the Space Interferometry Mission. Further improvements might be possible by rereducing the original photometric lightcurve using image subtraction or by obtaining new, higher-precision baseline photometry of the source. We show that the current data strongly limit scenarios in which the lens is a dark (i.e., brown-dwarf) companion to the observed M dwarf rather than being the M dwarf itself. These results set the stage for a confrontation between mass estimates of the M dwarf obtained from spectroscopic and photometric measurements and a mass measurement derived directly from the star's gravitational influence. This would be the first such confrontation for any isolated star other than the Sun.

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arXiv2004

v_\perp CMD

I present an Hipparcos color-magnitude diagram (CMD) that is color-coded by transverse velocity v_\perp. This illustrates the connection between the photometric and kinematic properties of various stellar populations in a manner that is particularly suitable to introductory astronomy courses.

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arXiv2004

Resolution of the MACHO-LMC-5 Puzzle: The Jerk-Parallax Microlens Degeneracy

By extending the constant-acceleration analysis of Smith, Mao, & Paczynski to include jerk, I show that microlens parallax measurements are subject to a four-fold discrete degeneracy. The new degeneracy is characterized by a projected velocity \tilde v_j = -(3/4)\cscβ_\ec(\cos^2ψ\sin^2β_\ec+\sin^2ψ)^{3/2}v_earth, where β_\ec is the ecliptic latitude, ψis the phase of the Earth's orbit relative to opposition at the time of the event maximum, and v_earth=30 km/s is the speed of the Earth. The degeneracy becomes important when the lens projected velocity \tilde v is of order \tilde v_j. For events toward the Large Magellanic Cloud, \tilde v_j\simeq (3/4)v_earth, so this degeneracy is important primarily for lenses in the Milky Way disk. In particular, it solves the puzzle of MACHO-LMC-5, whose microlens parallax measurement had yielded mass and distance determinations for the lens that were inconsistent with photometric estimates. Toward the Galactic bulge, \tilde v_j ranges from about 0.2 km/s at the solstice to about 200 km/s at the equinoxes, so the effect of the degeneracy depends strongly on the peak time of the event. The degeneracy applies mainly to events with Einstein timescales, t_E < yr/2pi.

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arXiv2004

KELT: The Kilodegree Extremely Little Telescope

Transits of bright stars offer a unique opportunity to study detailed properties of extrasolar planets that cannot be determined through radial-velocity observations. We propose a technique to find such systems using all-sky small-aperture transit surveys. The optimal telescope design for finding transits of bright stars is a 5 cm ``telescope'' with a 4k x 4k camera. We are currently building such a system and expect to detect ~10 bright star transits after one year of operation.

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arXiv2003

Testing Bimodal Planet Formation

We suggest that the observed break in giant-planet frequency as a function of host metallicity at Z=0.02 may be a reflection of bimodal planet formation. We search for signatures of this bimodality in the distributions of the planet eccentricities, periods, masses, and multiplicity. However, the low-metallicity sample is at present too small to test for any but the most severe differences in these two putative populations.

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arXiv2003

Using All-Sky Surveys to Find Planetary Transits

Transits of bright stars offer a unique opportunity to study detailed properties of extrasolar planets that cannot be determined through radial-velocity observations. We propose a new technique to find such systems using all-sky small-aperture transit surveys. We derive a general formula for the number of stars that can be probed for such systems as a function of the characteristics of the star, the planet, and the survey. We use this formula to derive the optimal telescope design for finding transits of bright stars: a 5 cm ``telescope'' with a 4k x 4k camera.

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arXiv2003

Proper Motion Catalog From SDSS \intersect USNO-B

We present a catalog of 345,000 stars with proper motions μ> 20 mas/yr and magnitudes r' <20, drawn from the intersection of the SDSS Data Release One and USNO-B. We first use SDSS quasars to correct the proper motions in each of the two source catalogs, finding that these corrections for systematics are comparable to the statistical errors. The combined proper motions have errors of σ_μ=4.0 mas/yr, significantly better than any previous catalog at these magnitudes. While cross-correlating SDSS and USNO-B removes the vast majority of the very large number of spurious proper-motion stars in each, some contamination remains, especially at faint magnitudes, r' > 19.5, and high proper motions. We present a diagrammatic method to estimate the level of contamination in selected subsets of the catalog, which should be useful for choosing appropriate selection criteria for various applications.

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arXiv2003

chi^2 and Linear Fits

The mathematics of linear fits is presented in covariant form. Topics include: correlated data, covariance matrices, joint fits to multiple data sets, constraints, and extension of the formalism to non-linear fits. A brief summary at the end provides a convenient crib sheet. These are somewhat amplified notes from a 90 minute lecture in a first-year graduate course. None of the results are new. They are presented here because they do not appear to be elsewhere available in compact form.

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